Crack Paths 2006

Determination of Bridging Stress from Bending of a Deep Notched Specimen

K. Mori1, I. Torigoe2 and S. Hashimura3

1 KumamotoUniversity, Faculty of Engineering, Department of Mechanical Engineering

2-39-1 Kurokami, Kumamoto,860-8555 JAPAN

kmori@mech.kumamoto-u.ac.jp

2 torigoe@kumamoto-u.ac.jp

3 hasimura@kurume-nct.ac.jp

ABSTRACT.A method to measure bridging stress by using bending test of a deep

notched specimen is developed in this paper. To obtain the bridging stress from the

integral equation which relates the bridging stress to the load, a numerical inverse

analysis method is also developed. By using the present method the authors evaluated

the grain-bridging stresses of polycrystalline alumina ceramics with the mean grain size of 3 Pm an 11 Pm. The obtained results can be summarized as follows: (1) the mean

grain size had no effect on the maximumbridging stress for alumina, (2) the correlation

was not observed between the maximumbridging stress and the bending strength for

alumina ceramics.

I N T R O D U C T I O N

Bridging stress occurring in the wake of a crack is effective to increase the fracture

toughness of structural materials. For instance, putting fibers into the material its

bridging stresses increases and fracture toughness increases. Therefore it is important to

have a reliable and easy method to evaluate bridging stress characteristics for the

material development.

Several methods to evaluate bridging stress characteristics have been proposed

in the past. There methods can be divided broadly into two types. One is to measure the

crack concerned. Amongthis type of methods, bridging stresses can be determined

either from crack opening displacement [1-4] or from compliance [5, 6]. This type of

methods can be further divided into three different methods in terms of loading

conditions [7-9].

In this study, an experimental method of measuring bridging stresses by using

the bending test of a deep-notched specimen, shown in Fig. 1, and the inverse analysis

of experimental data is developed. In the case of bending of deep-notched specimens, a

crack passes through the ligament stably [10]. Bridging materials keep resistance

against the load after a crack passed trough the ligament. Bridging stress characteristics

can be evaluated from this resistance against the load.

However, this resistance is expressed by an integral from under various opening

displacements in this method. Therefore, a numerical inverse analysis is developed to

obtain bridging stress characteristics from the integral equation.